Worksheet on Remainder Theorem

Practice the questions given in the worksheet on Remainder Theorem.


1. Use the Remainder Theorem, find the remainder when 4x\(^{3}\) - 3x\(^{2}\) + 2x - 4 is divided by x + 1.

2. If p(y) = y\(^{3}\) + y\(^{2}\) - 2y + 1, using Remainder Theorem, find the remainder, when p(y) is divided by (y – 3), find the value of p(a).

3. Find the remainder (without division) when

(a) x\(^{2}\) - 2x + 4 is divided by x - 1

(b) 2x\(^{3}\) - 3x\(^{2}\) + 7x - 8 is divided by x - 1


4. Use the Remainder Theorem, find the remainder when x\(^{4}\) - 3x\(^{2}\) + 4x - 12 is divided by x - 3.


5. Find the remainder (without division) when

(a) x\(^{3}\) + 4x + 2 is divisible by x + 2

(b) 4x\(^{3}\) - 3x\(^{2}\) + 5x + 4 is divided by 2x + 1

(c) 4x\(^{3}\) + 5x\(^{2}\) + 6x - 7 is divided by 2x - 1


6. What number should be added to x\(^{2}\) + 5 so that the resulting polynomial leaves the remainder 3 when divided by x + 3?

7. Use the Remainder Theorem, find the remainder when 4x\(^{3}\) - 3x\(^{2}\) + 2x - 4 is divided by x + 1.

8. What number should be subtracted from 3x\(^{2}\) + 5x so that the resulting polynomial leaves the remainder 1 when divided by 2x + 5?

9. Use the Remainder Theorem, find the remainder when x\(^{6}\) + 3x\(^{2}\) + 10 is divided by x - 2.

10.  Find a if the remainder is a when x\(^{3}\) + 3x\(^{2}\) - ax + 3 is divided by x - 2.

11. If the polynomials ax\(^{3}\) + 4x\(^{2}\) + 3x – 4 and x\(^{3}\) - 4x + a leave the same remainder when divided by (x - 3), find the value of a.

12. Find the value of k if the remainder is -3 when kx\(^{3}\) + 8x\(^{2}\) - 4x + 10 is divided by x +1.

13. If both ax\(^{3}\) + 2x\(^{2}\) - 3 and x\(^{2}\) - ax + 4 leave the same remainder when divided by x - 2, find a.


Answers for the worksheet on Remainder Theorem are given below:


Answers:


1. -13

2. 31, a\(^{3}\) + a\(^{2}\) - 2a + 1

3. (a) 3

(b) -2


4. 54

5. (a) -14

(b) \(\frac{1}{4}\)

(c) -\(\frac{9}{4}\)


6. -11

7. -13

8. \(\frac{21}{4}\)

9. 86

10. \(\frac{23}{3}\)

11. a = -1.

12. 25

13. \(\frac{3}{10}\)

● Factorization















10th Grade Math

From Worksheet on Remainder Theorem to HOME


New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.



Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



Share this page: What’s this?

Recent Articles

  1. Adding 5-digit Numbers with Regrouping | 5-digit Addition |Addition

    Mar 18, 24 02:31 PM

    Adding 5-digit Numbers with Regrouping
    We will learn adding 5-digit numbers with regrouping. We have learnt the addition of 4-digit numbers with regrouping and now in the same way we will do addition of 5-digit numbers with regrouping. We…

    Read More

  2. Adding 4-digit Numbers with Regrouping | 4-digit Addition |Addition

    Mar 18, 24 12:19 PM

    Adding 4-digit Numbers with Regrouping
    We will learn adding 4-digit numbers with regrouping. Addition of 4-digit numbers can be done in the same way as we do addition of smaller numbers. We first arrange the numbers one below the other in…

    Read More

  3. Worksheet on Adding 4-digit Numbers without Regrouping | Answers |Math

    Mar 16, 24 05:02 PM

    Missing Digits in Addition
    In worksheet on adding 4-digit numbers without regrouping we will solve the addition of 4-digit numbers without regrouping or without carrying, 4-digit vertical addition, arrange in columns and add an…

    Read More

  4. Adding 4-digit Numbers without Regrouping | 4-digit Addition |Addition

    Mar 15, 24 04:52 PM

    Adding 4-digit Numbers without Regrouping
    We will learn adding 4-digit numbers without regrouping. We first arrange the numbers one below the other in place value columns and then add the digits under each column as shown in the following exa…

    Read More

  5. Addition of Three 3-Digit Numbers | With and With out Regrouping |Math

    Mar 15, 24 04:33 PM

    Addition of Three 3-Digit Numbers Without Regrouping
    Without regrouping: Adding three 3-digit numbers is same as adding two 3-digit numbers.

    Read More